Some remarks on multicategories and additive categories
Category Theory
2013-04-11 v1
Abstract
Categories are coreflectively embedded in multicategories via the "discrete cocone" construction, the right adjoint being given by the monoid construction. Furthermore, the adjunction lifts to the "cartesian level": preadditive categories are coreflectively embedded (as theories for many-sorted modules) in cartesian multicategories (general algebraic theories). In particular, one gets a direct link between two ways of considering modules over a rig, namely as additive functors valued in commutative monoids or as models of the theory generated by the rig itself.
Cite
@article{arxiv.1304.3033,
title = {Some remarks on multicategories and additive categories},
author = {Claudio Pisani},
journal= {arXiv preprint arXiv:1304.3033},
year = {2013}
}
Comments
15 pages, 1 figure